Adds useAppBadge alongside the existing useFaviconBadge, mounted from the
same FaviconBadge component and gated by the same faviconUnreadBadge
setting. Targets the separate icon Chrome/Edge/WebKit show for an
installed PWA (taskbar/dock/Home Screen/pinned-app-shortcut), which does
not react to favicon changes at all - a merely pinned browser tab is
unaffected, only an actually installed app.
No unmount cleanup: the badge is scoped to the installed app/origin, not
to this component or window, so clearing on every unmount would blank
another still-open window's accurate badge. A count of zero or the
setting being off already clears it through the main effect.